Actually, I think I’ve just done it. All you need to do is use the Twitter Timeline widget. Then use the link in that to go and create a widget on Twitter using their Widgets Configurator (https://twitter.com/settings/widgets/).

In that configurator, click the ‘search’ tab to create a search widget, enter your base url as a search term, customise any other options and copy the ID from the code generated (alternatively it’s also in the URL after widgets/)

Go back to WordPress and your widget settings and paste that ID number. Save.